Small area estimation via basic area level model

Generates small area estimates by smoothing direct estimates using an area level model

svysmoothArea(
  formula,
  domain,
  design = NULL,
  adj.mat = NULL,
  X.domain = NULL,
  direct.est = NULL,
  domain.size = NULL,
  transform = c("identity", "logit", "log"),
  pc.u = 1,
  pc.alpha = 0.01,
  pc.u.phi = 0.5,
  pc.alpha.phi = 2/3,
  level = 0.95,
  n.sample = 250,
  var.tol = 1e-10,
  return.samples = FALSE,...
)

Arguments

formula

An object of class 'formula' describing the model to be fitted. If direct.est is specified, the right hand side of the formula is not necessary.

domain

One-sided formula specifying factors containing domain labels

design

An object of class "svydesign" containing the data for the model

adj.mat

Adjacency matrix with rownames matching the domain labels. If set to NULL, the IID spatial effect will be used.

X.domain

Data frame of areal covariates. One of the column names needs to match the name of the domain variable, in order to be linked to the data input. Currently only supporting time-invariant covariates.

direct.est

Data frame of direct estimates, with first column containing the domain variable, second column containing direct estimate, and third column containing the variance of direct estimate.

domain.size

Data frame of domain sizes. One of the column names needs to match the name of the domain variable, in order to be linked to the data input and there must be a column names 'size' containing domain sizes.

transform

Optional transformation applied to the direct estimates before fitting area level model. The default option is no transformation, but logit and log are implemented.

pc.u

Hyperparameter U for the PC prior on precisions. See the INLA documentation for more details on the parameterization.

pc.alpha

Hyperparameter alpha for the PC prior on precisions.

pc.u.phi

Hyperparameter U for the PC prior on the mixture probability phi in BYM2 model.

pc.alpha.phi

Hyperparameter alpha for the PC prior on the mixture probability phi in BYM2 model.

level

The specified level for the posterior credible intervals

n.sample

Number of draws from posterior used to compute summaries

var.tol

Tolerance parameter; if variance of an area's direct estimator is below this value, that direct estimator is dropped from model

return.samples

If TRUE, return matrix of posterior samples of area level quantities

...

for future methods

Value

A svysae object

Details

The basic area level model is a Bayesian version of the Fay-Herriot model (Fay & Herriot,1979). It treats direct estimates of small area quantities as response data and explicitly models differences between areas using covariate information and random effects. The Fay-Herriot model can be viewed as a two-stage model: in the first stage, a sampling model represents the sampling variability of a direct estimator and in the second stage, a linking model describes the between area differences in small area quantities. More detail is given in section 4 of Mercer et al (2015).

See also

The survey-sae vignette

References

Fay, Robert E., and Roger A. Herriot. (1979). Estimates of Income for Small Places: An Application of James-Stein Procedures to Census Data. Journal of the American Statistical Association 74 (366a): 269-77.

Mercer LD, Wakefield J, Pantazis A, Lutambi AM, Masanja H, Clark S. Space-Time Smoothing of Complex Survey Data: Small Area Estimation for Child Mortality. Ann Appl Stat. 2015 Dec;9(4):1889-1905. https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4959836/

Examples

## artificial data from SUMMER package
## Uses too many cores for a CRAN example

if (FALSE) { # \dontrun{
 hasSUMMER<-tryCatch({
   data("DemoData2",package="SUMMER")
   data("DemoMap2", package="SUMMER")
  }, error=function(e) FALSE)

if (!isFALSE(hasSUMMER)){
 library(survey)
 des0 <- svydesign(ids = ~clustid+id, strata = ~strata,
                  weights = ~weights, data = DemoData2, nest = TRUE)
 Xmat <- aggregate(age~region, data = DemoData2, FUN = mean)

 cts.cov.res <- svysmoothArea(tobacco.use ~ age, 
                          domain = ~region,
                          design = des0,
                          adj.mat = DemoMap2$Amat, 
                          X.domain = Xmat,
                          pc.u = 1,
                          pc.alpha = 0.01,
                          pc.u.phi = 0.5,
                          pc.alpha.phi = 2/3)
 print(cts.cov.res)
 plot(cts.cov.res)
}
} # }